Position Barlow Lens for 3x Image w/ Focal Length -0.05m

[recon9]

1. I am trying to figure out a problem involving a barlow lens in a telescope. All I know is that the focal length of the lens is -0.05m. I want to know where to place the barlow lens in front of the image created by the first lens (as if the barlow wasnt there) in order to get an image 3x the size as the image created by the first lens(as if the barlow wasnt there)



2. I know that (1/S)+(1/S')=(1/f) and m = -(S'/S).



3. I drew a diagram and filled in some variables then tried to equate the above solutions but that gave me an answer with an unknown still in it.

 

[Nate810]

4. To solve this problem, we can use the formula m = -(S'/S)+(1/f). This tells us that S' = -mS + (1/f). We can then use this equation to calculate S' given the focal length of the lens (f) and the magnification (m) of the barlow lens. In this case, f = -0.05m and m = 3. Therefore, S' = -(3)(S) + (1/-0.05) = -3S + 20. So the barlow lens should be placed 20 cm in front of the image created by the first lens to get an image 3x the size as the image created by the first lens.

 

[m2003]

I understand your confusion and I am happy to assist you in solving this problem. Firstly, it is important to note that the focal length of a lens is typically given as a positive value, so the -0.05m value you have provided may need to be double-checked. Assuming it is correct, we can proceed with finding the position of the barlow lens for a 3x image.

To begin, let us define some variables. Let S be the distance from the first lens to the object, S' be the distance from the first lens to the image, and f be the focal length of the first lens. We also know that the magnification, m, is equal to -(S'/S).

Using the equation (1/S)+(1/S')=(1/f), we can rearrange to solve for S' as S' = f(S+f)/S. Since we want a 3x image, we know that S' must be three times the distance of S. Therefore, we can set up the equation 3S = f(S+f)/S and solve for S to find the distance from the first lens to the object.

Once we have the value for S, we can use the equation S' = f(S+f)/S to find the position of the barlow lens. This will be the distance from the first lens to the barlow lens.

I hope this helps you in solving your problem. If you have any further questions, please do not hesitate to ask. As scientists, it is important to constantly question and seek understanding. Good luck with your research!